Entropic elasticity and negative thermal expansion in ScF₃

Negative thermal expansion (NTE) is common in polymers and biomolecules, where its origin can be traced to entropic elasticity, but is rare in solids where it is desirable for applications. We report pair distribution function (PDF) analysis of neutron total scattering tracking the local structure and relative atomic positions in ScF₃ as it shrinks with increasing temperature. In agreement with previous Xray studies^1,2, we find that Sc-F bond slightly expands on warming, while the lattice spacing decreases. The correlation in positions of the neighbor F atoms rapidly fades on warming, consistent with simple model of F transverse thermal motion constrained only by the rigid Sc-F bond. This indicates that entropic stiffness rendered by strong Sc-F bond is at the origin of NTE in ScF₃. We thus observe universality of the NTE phenomenon across hard and soft matter, which opens new avenues for predictive modelling of this effect in solids.
1. B. K. Greve, et al, J. Am. Chem. Soc. 132, 15496 (2010)
2. L. Hu, et al, J. Am. Chem. Soc. 138, 8320 (2016)